This proposal revolves around the development of new statistical methods and their application to studies involving cancer and nutrition. The following broad topics will be considered. Diet and Colon Carcinogenesis: We will develop semi-parametric statistical methods for hierarchical functional data to analyze a new series of studies, done at the cellular level, involving diet, apoptosis, cellular response and colon carcinogenesis. Our approach allows understanding of the effects of cell position in the colonic crypts, as well as incorporating crypt signaling, i.e., correlations of response among the crypts themselves. A special case of our approach includes new hierarchical functional measurement error models. Analysis of Dietary Intake Data: In conjunction with researchers at the NCI, we have developed access to a number of exciting dietary intake data sets, including a major biomarker study, a major surveillance study and a major prospective cohort study. Our research includes the use of multiple nutrients to estimate aspects of dietary measurement error simultaneously: with biologically relevant assumptions we will show great gains in efficiency over the common single nutrient approach. For food group data, we will develop a novel model that allows for people who never eat particular foods over a fixed time period, and we will apply this model to dietary surveillance and to prospective studies. These problems motivate a new general semiparametric likelihood framework and a new theory for model selection in this complex semiparametric framework. Semiparametric Methods: First, we are motivated by semiparametric modeling of correlated and longitudinal data, and we will develop a general framework for deriving semiparametric efficient estimates that solve problems not previously considered. We will also develop methods for semiparametric inference in measurement error problems, going far beyond what is available in the literature. The second approach arises in case-control studies with measurement error, including gene-environment interaction studies. We will consider the case that genetic and environmental factors are independent in the population, possibly after conditioning on factors to account for population stratification. We will develop methods that allow for measurement error in environmental factors, missing genotype data, analysis of haplotype data without phases and genotyping errors.